A modified hyperbolic tangent equation to determine equilibrium shape of headland bay beaches

Jonathan Kemp, Benoit Vandeputte, Thomas Eccleshall, Richard Simons, Peter Troch

Research output: Contribution to journalConference articlepeer-review

1 Scopus citations


When designing any artificial beach, it’s desirable to avoid (or minimise) future maintenance commitments by arranging the initial beach planshape so that it remains in equilibrium given the incident wave climate. Headlands bays, or embayments, where a sandy beach is held between two erosion resistant headlands, tend to evolve to a stable beach planshape with little movement of the beach contours over time. Several empirical bay shape equations have been derived to fit curves to the shoreline of headland bay beaches. One of the most widely adopted empirical equations is the parabolic bay shape equation, as it is the only equation that directly links the shoreline positions to the predominant wave direction and the point of diffraction. However, the main limitation with the application of the parabolic bay shape equation is locating the downcoast control point. As a result of research presented in this paper a new equation, based on the hyperbolic tangent shape equation was developed, which eliminates the requirement of placing the down coast control point and relies on defining a minimum beach width instead. This modified equation was incorporated into a new ArcGIS tool.

Original languageEnglish (US)
JournalProceedings of the Coastal Engineering Conference
Issue number2018
StatePublished - 2018
Externally publishedYes
Event36th International Conference on Coastal Engineering, ICCE 2018 - Baltimore, United States
Duration: Jul 30 2018Aug 3 2018


  • Coastal Engineering
  • Headland Bays
  • Stable beaches

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Ocean Engineering
  • Oceanography


Dive into the research topics of 'A modified hyperbolic tangent equation to determine equilibrium shape of headland bay beaches'. Together they form a unique fingerprint.

Cite this